Identifying Decreasing Domains in a Piecewise Function Graph

Decreasing Functions with Piecewise Intervals

In what domain is the function decreasing?

–1–1–1111–1–1–1111000

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Step-by-step video solution

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00:00 Find the domain where the function decreases
00:04 The function decreases when X values increase and Y values decrease
00:10 First, let's find the domains of increase
00:15 Now let's find the domains of decrease
00:23 Let's identify exactly when the function decreases
00:33 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

In what domain is the function decreasing?

–1–1–1111–1–1–1111000

2

Step-by-step solution

Let's remember that the function increases when X values and Y values increase simultaneously.

On the other hand, the function decreases when X values increase and Y values decrease simultaneously.

In the given graph, we notice that the function decreases in two different places on the graph.

The first time it decreases in the domain where 0>x>1 0 > x > -1 and the second time it decreases in the domain where

x>1 x > 1

This means that in these domains, the Y values are decreasing.

3

Final Answer

0>x>1,x>1 0>x>-1,x>1

Key Points to Remember

Essential concepts to master this topic
  • Definition: Function decreases when x increases but y decreases
  • Technique: Find intervals where graph slopes downward from left to right
  • Check: Verify both intervals: -1 < x < 0 and x > 1 show decreasing ✓

Common Mistakes

Avoid these frequent errors
  • Identifying only one decreasing interval
    Don't stop after finding the first decreasing section = missing part of the answer! Piecewise functions can decrease in multiple separate intervals. Always scan the entire graph from left to right to identify all decreasing domains.

Practice Quiz

Test your knowledge with interactive questions

Is the function in the graph decreasing? yx

FAQ

Everything you need to know about this question

How do I know if a function is decreasing?

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A function is decreasing when the graph goes downward as you move from left to right. Imagine walking along the graph - if you're going downhill, the function is decreasing!

What's the difference between -1 < x < 0 and x > 1?

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These are two separate intervals where the function decreases. The first is between -1 and 0, and the second starts at 1 and continues right. Both must be included in your answer.

Why can't I write this as one continuous interval?

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Because the function increases between x = 0 and x = 1! You can't combine intervals where the function behaves differently. Each decreasing section must be written separately.

Do I include the endpoints where the function changes direction?

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Look carefully at the graph! At turning points, the function usually stops decreasing or increasing. These transition points are typically not included in the decreasing intervals.

What if the graph has curves instead of straight lines?

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The same rule applies! Whether straight or curved, if the graph goes downward from left to right in that section, the function is decreasing in that interval.

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